This article provides a guide to choosing
between the discrete Kolmogorov-Smirnov statistic and the root-mean-square.

William Perkins, Gary Simon, and Mark Tygert,
"Computing the asymptotic power of a Euclidean-distance test
for goodness-of-fit,"
Technical Report 1206.6378, arXiv, June 2012:
pdf.

This article provides an efficient numerical method for plotting
the asymptotic power function of a root-mean-square test
for goodness-of-fit in the limit of large numbers of observations
(as a function of the significance level).
This follows up on our earlier paper,
"χ2 and classical exact tests often wildly misreport
significance; the remedy lies in computers," which is available below.

This article analyzes homogeneity in contingency-tables/cross-tabulations
using the approach of our earlier paper,
"χ2 and classical exact tests often wildly misreport
significance; the remedy lies in computers," which is available below.

Many thanks to Professor F. W. J. Olver of the University of Maryland
for pointing out formula 57.21.1
in E. R. Hansen's A Table of Series and Products,
which provides a more general formulation of one of the analogues
(thus obviating the need for publishing this technical report).